Geogebra (Features and Possiblities)

1. Geogebra
(Features & Possibilities)
Kapil Pundir, PGT Maths
K.V. Loktak, Manipur
8077291675

2. Revision
• A chapter of Class 11 / 12 is allotted to you.
• Create a word file in your computer with chapter name as file name
• Type all the formulas of given chapter in your word file.
• Also mention your name and KV in file.

4. GEOmetry + alGEBRA
Started by Markus Hohenwarter in 2001 as part of his master's thesis at
the University of Salzburg, Austria
In December, 2021 acquired by Byju’s India in $100 million.
Open Source Software
Free to use

5. Basic
Features of
Geogebra
Download
& Install
Geogebra
Possibilities
Of
Geogebra
Table of Content

6. Basic
Features of
Geogebra
Download
& Install
Geogebra
Possibilities
Of
Geogebra

7. Visualizing Graphs

8. Trigonometric Functions

9. Venn Diagrams

10. Application of Matrices

11. Area Under Curve

12. Continuity

13. Differentiability

14. WWW.GEOGEBRA.ORG

15. Basic
Features of
Geogebra
Download
& Install
Geogebra
Possibilities
Of
Geogebra

16. Steps for Downloading Geogebra
(Android)
Play
Store
Geogebra
Suite
Install

17. Steps for Downloading Geogebra
(Windows)
www.Geogebra.org
App Downloads
Calculator Suite
Download Install

18. Basic
Features of
Geogebra
Download
& Install
Geogebra
Possibilities
Of
Geogebra

22. How to useTools

23. Starting with basics
• Graph of functions
• Trace of functions
• Vertical line test for function (and finding its domain)
• Inverse of graph by reflecting about the line
• Combination of functions
• Shifting expansion and contraction of graph
• Even and Odd functions
• Horizontal line test for injective function (and finding its range)

24. Graph of functions
• Go to Algebra view
• Type the function in input
Try yourself
• Construct the graph of following functions
• 1. 𝑥3
• 2. |𝑥|
• 3.
1
𝑥
• 4. sin(𝑥)

25. Trace of functions
• • Define a slider a
• • In input box type (𝑎, 𝑎2)
• • Apply enter key
• •Then you will get a pointA, right click on it
• • Select trace on
• • Right click on slider a
• • Select animation
Try yourself
• Construct the graph of following functions, using trace of a point input method
• 1. 𝑥3
• 2. |𝑥|
• 3.
1
𝑥
• 4. sin(𝑥)

26. Vertical line test for function (and finding its domain)
• Draw graph of a function
• Make a point A on X axis
• Make line at point A perpendicular to X axis
• Make intersection of function and line
• Check it for circle and check is it a function
Try yourself
• Construct the graph of following functions, and use vertical line test
• 1. 𝑥3
• 2. |𝑥|
• 3.
1
𝑥
• 4. sin(𝑥)

27. Inverse of graph by reflecting about the line
• Draw graph of a function
• Make line 𝑦 = 𝑥
• In tools menu, Select reflect about line option
• Click on function and then line of reflection
Try yourself
• Construct the graph of following functions, and try to find inverse
• 1. 𝑥3
• 2. |𝑥|
• 3. 𝑒𝑥
• 4. sin(𝑥)

28. Combination of functions
• Make two functions f and g
• In algebra view, type 𝑓 𝑔 𝑥 and 𝑔(𝑓 𝑥 )
Try yourself
• Construct the graph of following functions, and try to find
𝑓 𝑔 𝑥 and 𝑔(𝑓 𝑥 )
• 1. 𝑓 𝑥 = 𝑥2, 𝑔 𝑥 = cos 𝑥
• 2. 𝑓 𝑥 = 2𝑥 + 3, 𝑔 𝑥 =
𝑥−3
2

29. Shifting, expansion and contraction of graph
• Draw graph of a function f(x)
• Make a slider 𝑎
• Make function 𝑎 × 𝑓 𝑥 , 𝑓 𝑥 + 𝑎, 𝑓 𝑥 + 𝑎
• Observe the function while changing the value of slider.
Try yourself
• Construct the graph of following functions, and try Shifting, expansion and
contraction
• 1. 𝑥3
• 2. |𝑥|
• 3. 𝑒𝑥
• 4. sin(𝑥)

30. Even and Odd functions
• Draw graph of a function f(x)
• Draw function f(-x)
• Observe the relation between f(x) and f(-x)
Try yourself
• Construct the graph of following functions, and try Shifting, expansion and
contraction
• 1. 𝑥3
• 2. |𝑥|
• 3. 𝑒𝑥
• 4. sin(𝑥)
• Try some other even, odd functions

31. Horizontal line test for injective function (and finding its range)
• Draw graph of a function
• Make a point A on X axis
• Make line at point A perpendicular to X axis
• Make intersection of function and line
• Check it for circle and check is it a funciton
Try yourself
• Construct the graph of following functions, and try Shifting, expansion and
contraction
• 1. 𝑥3
• 2. |𝑥|
• 3. 𝑒𝑥
• 4. sin(𝑥)

32. For all Geogebra files
• Go to website www.sajhishiksh.in

33. Kapil Pundir, PGT Maths
K.V. Loktak, Manipur
8077291675